Question

When solving Linear Equations (Initial value problems, Boundary value problems, Homogeneous/nonhomogeneous equations) and solving undetermined coefficients does the order of C1 and C2 matter? For example m=+or-3 so y=C1e^3x+C2e^-3x

Answer 1

When they are just undetermined coefficients, no. You can name them whatever you want. That only matters after the IVP/BVP is solved which is when the values of these coefficients are determined.
Though I'd say its probably bad practice to name your variables C1 and C2 when you solve for them and want to leave your equation in a simple form.

Answer 2

They are just constants. You can make then whatever you want them to be.

Answer 3

Thank you, I thought so but I needed to be sure.